Weight and Interface Strength

This section defines and describes measurement techniques for several
performance characteristics deemed appropriate for plastic products.
While there are many subjective ways of classifying and quantifying a
product's performance and quality, we will stick to only a few of the
more well-defined aspects that can be physically measured. Certain
characteristics that are important in plastic product design will be
quantified and measured as performance aspects. For example, parameters
such as weight and strength are both relevant and quantifiable, so they
will be considered in this model.

For clarity, we will henceforth define a "performance aspect" (PA) as a
measurable physical quality of a plastic product assembly that
non-subjectively and non-arbitrarily quantifies its desirability.
Therefore, each PA will have actual physical units (e.g. grams,
millimeters, etc&) used to describe it. The following subsections will
define the relevant PA's and describe how to measure and/or compute
them.

Performance Aspect 1: Weight

In most applications, weight reduction is an important goal. By
minimizing the total weight of a product, significant performance
increases (as well as cost reduction) can be achieved. In general,
minimizing weight without sacrificing other performance aspects (e.g.
strength) is a common goal for most products.

The computation of a product's total weight is simple. Although the
actual weight of each shot can vary because the molded resin density
varies throughout the part due to processing conditions, the nominal
part weight can easily be calculated from its volume and the resin's
average density. Hence, the nominal part weight will be used as PA 1.
This value can be instantaneously and accurately be automatically
calculated from the CAD file of the assembly. For MMM and SMM&A,
the total product weight is the sum of both parts A and B, and any
fasteners/adhesives. Most popular CAD systems will output the total
weight of an assembly given the materials and/or densities of the
components. We will use ounces as our measurement units for weight.

Weight is a valid PA because weight minimization is a common goal
across all product classes. It is a proven performance measurement, and
one that is calculated with relative ease.

Performance Aspect 2: Interface Strength

The term "strength" can refer to a wide range of physical
characteristics defining how well an object can sustain loads and
moments. There are many material properties and corresponding physical
tests that can be used to form some measure of the strength of a
component or assembly.

Definition of Interface Strength

Here we will use the strength of the interface as our PA; that is, how
hard it is to separate components A and B at their mutual interface. It
should be noted that here, the definition of an interface will be
loosened to include any section on the assembly where the separate
materials meet, whether there is microscopic bonding or not. This way,
articulated parts such as hinges or joints can have a strength PA
associated with them.

Interface separation strength was chosen as a PA to represent strength
since it is relatively straightforward and universal for the type of
assemblies under analysis. This is because all two-material assemblies
posses an interface, and separation is a defining and possible failure
mode for two-material assemblies. While fracture of either or both
materials is also a possible failure mode, interface separation is
probably more likely (unless the interface is optimally designed) and
is a defining characteristic of assemblies. Regardless, the strength
test should allow for all possible failure modes. Furthermore, this PA
was chosen to coincide with the physical tests commonly used in
industry to characterize the strength of various material interfaces.
Hence, interface strength will be defined as the force or moment
required to produce one of the following three failure modes:

1) Complete separation of the components A and B along their common interface ("mode AB")

2) Fracture of component A ("mode A")

3) Fracture of component B ("mode B")

Although there are actually five possible types of failure mechanisms,
only two mechanisms (embodied in the three failure modes listed above)
are sufficient to characterize strength for the purposes of this model.
This is based off observance of typical failed multi-material assembly
specimens.

Types of Interface Strength Tests

Like all other measures of strength, interface strength could be
characterized by a number of different attributes that define how well
the interface performs under a particular loading scenario. Typically,
the interface could is pulled apart (tension), or twisted apart
(torsion). These two types of tests, among others, are valid strength
attributes, but we will focus on only tensile and torsional forces here
for the sake of brevity. This is because in industry tests, shear and
normal strength are the most commonly-tested attributes. The model
could quite easily be adapted to include other strength tests.

In addition to specifying the types of strength tests to use, the
appropriate method of conducting such tests must also be defined. That
is, the nature and directions of loadings and the type and location of
restraints must be specified for each type of test. Unfortunately, it
can be quite difficult to define a set of appropriate physical tests
that can be universally applied to all types of assemblies, regardless
of geometry or intended functionality. As with most physical tests or
finite element simulations, the appropriate set of testing conditions
should be chosen based on the product's structure as well as the
expected conditions it will experience under normal use.

These conditions are typically chosen based on common sense and
experience. For example, although a steel bolt could theoretically be
loaded in an infinite number of arbitrary directions, tensile testing
is usually conducted parallel to the bolt's axis, because this is the
type of loading it would normally experience. Similar reasoning should
be used to determine the appropriate loading conditions for plastic
assemblies. For example, when tensile testing a hinge box, it seems
reasonable to assume that the assembly would first break somewhere
along the hinge. Therefore, a valid tensile test would attempt to pull
the lid apart from the base by loading the lid parallel to its surface
(and resultantly intersecting the hinge's center), as shown below in
Figure 1.

It is highly recommended that each assembly be carefully analyzed and
assigned an appropriate set of physical tests which are specifically
catered to the form and function of the product. However, a set of
universal physical tests will next be prescribed for the sake of
consistency as well as the relative comparison purposes of this model.

Prescribed Loading and Constraints

The model will take advantage of the way the products are assembled to
establish the proper loading directions and restraints. In essence, the
loads will be applied in a direction coinciding with assembly
direction. In SMM&A, one component is usually inserted into another
fixed component along a single direction. This insertion vector will be
used as the primary loading direction for the SMM&A variant. For
MMM, although there is no actual assembly, the nature of rotary platen
MSM generally causes one material to be stacked directly on top of the
other during the injection process. This direction, the mold's opening
direction, will be used as the primary loading direction for the MMM
variant. It should be noted that while the directions chosen for each
variant could be different, in general, they will be identical, due to
the geometric similarity between variants. For example, both hinge box
variants have the same basic geometry, so they could be tested using
the same loading directions. Furthermore, the same direction will be
used to represent both the resultant tensile and torsional loads.
Torsional loads are caused by moments which are uniquely defined by a
vector perpendicular to the plane of rotation using the right hand
rule. The moment vector will hence be collinear with the tension force
vector.

Instead of assigning restraints (e.g. fixed surfaces or edges), the
assemblies will be considered unrestrained with equal and opposite
loadings. That is, the same forces will be applied in opposing
directions on parts A and B to keep the entire assembly fixed in space.

Figure 2 shows two examples of choosing the proper loading direction
based on the mold opening direction and insertion direction. It can be
seen that the chosen loading directions are the most natural ones for
the separation of the two parts. This is simply a result of the fact
that they are put together along these same directions. While the
figure only shows resultant tensile load pairs (equal and opposite), it
should be noted that the loading would actually be manifested as a
distributed loading over the entire exposed surfaces of the parts.
These surface stresses are omitted from the figure for clarity.

The resultant load vector for a torsional force would look the same as
that for the tensional loading. For the examples of Figure 2, the
resultant moment vectors would also be vertical, and the resulting
shear stress would tend to distort the part surfaces tangentially (in a
horizontal circular path perpendicular to the page).

Conducting the Strength Tests

Actually conducting tensile and torsional tests on manufactured or
prototyped assemblies would be physically difficult, cost prohibitive,
and most importantly, it would negate the purpose of the model, which
is to provide designers with performance estimates early on in the
product development stages. Fortunately, computational mechanics allows
designers to test their ideas before they are ever produced. Most CAD
packages offer comprehensive finite element analysis (FEA) plug-ins
that allow a range of physical testing on single parts or entire
assemblies.

This model requires the use "virtual testing" through the use of such
FEA packages to determine the tensile and torsional strength of the
assemblies under comparison. It is actually a trivial matter to run the
physical simulations on CAD files once the loads and restraints have
been appropriately prescribed as discussed above. Unfortunately, most
software has trouble accurately modeling either chemical bonds or
adhesive bonding, the former of which is essential in most assemblies
produced via MMM. This shortcoming makes it difficult to obtain
accurate strength estimates for MM assemblies, which typically posses
combination locking and chemical interfaces. Furthermore, it is
possible to have purely chemical interfaces, which would result in
meaningless strength values of zero from standard FEA simulations which
only recognize mechanical locking.

In order to get around this difficulty, interface strength will be
broken up into several independent subsidiary PA's rather than
attempting to estimate the absolute interface strength. In stead of one
load value representing total strength, we will split it into the
following six independent PA's:

Of the above six PA's, the first two are determined through FEA
simulations, while the second two (and if necessary, the optional
remaining two) are determined through actual physical testing on
standardized specimens. Although physical testing on the actual
assemblies is cost and time prohibitive, testving of standard specimens
is straightforward as their molds should be readily available. All that
is required is a quick molding run using the desired resin combinations
on the existing MS molds for making the test specimens.

The first two PA's measure the specific mechanical strength of the
interface, which depends solely on its geometry. The remaining four
PA's measure the generic adhesion strength between the two materials.
This strength is based solely on the polymers' chemical compatibility
as well as the resin processing conditions used to mold both shots.
While the actual chemical bond strength depends on many parameters such
as the exact resin grade, the presence of fillers/colorants, and the
specific processing conditions, several resin manufacturers have
published independent results of material compatibility tests, such as
the one shown in Figure 3.

While charts such as the one above are useful as rough guides for
determining the applicability of various resin combinations, it is
strongly recommended that independent physical testing be conducted on
potential resin combinations for the products under analysis. Simple
test specimens should be molded under identical processing conditions
as the intended product and physically tested to accurately determine
the relative interface bonding strengths. Testing methods for PA's 2a
through 2f are detailed below.

These two PA's represent the maximum tensional/torsional load the
assembly could sustain before failure, assuming there is no chemical
bonding along the interface. These force values are calculated using
any 3D FEA package (e.g. Pro/Mechanica, ANYSYS, COSMOSWorks, etc&). The
tensional and torsional strengths must be determined through separate
simulations. The process is typically conducted as follows:

1) All of the materials are defined, including those of parts A and B and any fasteners.

2) No constraints should be set so that the assembly remains unfixed as described above.

3) The loading directions are prescribed as discussed above. The loads
can be applied as distributed loadings (surface pressures) over all of
the exposed surfaces of the assemblies, so that the resultant load is
parallel to either the mold opening direction or the insertion
direction (depending on the variant). An example of this type of
loading is shown below in Figure 4.

4) Finally, the simulation is run to obtain either the tensional or
torsional locking strength of the assembly [lbs] (PA's 2a and 2b,
respectively).

It should be noted that currently, standard FEA packages are unable to
accurately model bonded assemblies such as the MMM variants under
consideration. Therefore, it must emphasized that the simulations
suggested here are only used to indicate the relative locking strength
of the assemblies. The actual bonded assemblies may perform quite
differently in reality due to complex physical mechanisms such as
bonded ligament failure [22].

PA's 2c and 2d: Shear/Peeling Chemical Interface Strengths

These two strength tests measure how well the chemical interfaces
resist shear stresses and peeling, respectively. These are the most
commonly-used PA's by the MSM industry. The physical tests are
conducted on simple two-shot specimens, which are shown below in Figure 5:

The shear (lap-joint) test specimen (Figure 5a) is loaded with an
increasing tensile force until a critical failure load, , at which the
two materials separate along the flat interface. The peeling test
specimen (Figure 5b) is loaded with a tensile force perpendicular to
the flat interface until a critical failure load, , at which the
materials begins to peel apart. This load is then increased until total
separation of the interface. Both PA 2c and 2d can be uniquely defined
by their corresponding failure loads, and [lbs], respectively. The
actual dimensions of the test specimens is unimportant, as long as they
are consistent throughout all tests and feasibly made using the same MS
equipment that would produce the actual assemblies.

PA's 2e and 2f: Tensile/Torsional Chemical Interface Strengths

While some may argue that the two physical tests specimens discussed
above are adequate to completely determine two materials'
compatibility, an optional third type of test specimen is proposed in
order to determine the purely tensional or torsional chemical interface
strength. These optional tests are recommended in order to more closely
match the loading conditions prescribed in the FEA simulations. The
specimen geometry, as illustrated in Figure 6, consists of simple
circular interfaces which will be pulled apart or twisted apart from
pure tensional or torsional loads.

As with the previous two test specimens, the third test specimen can be
used to determine measures for PA's 2e and 2f. These PA's are uniquely
defined by the failure loads respectively.

Validity of Performance Aspect 2

The tests recommended above should yield valid measures of relative
strength between assemblies as they are just expanded forms of tests
proven in the MS industry. Both the FEA simulations and standardized
tests are common methods of evaluating strength of plastic components
used today.

The methodology for testing interface strength as well suggested
optional tests comes directly from experimental results of interfacial
strength testing [Bru04]. MMO's were molded with various interface
geometries and bonding characteristics and then destroyed via tensile
testing and analyzed using digital image correlation (DIC) in order to
understand the fundamental physics behind MMO interface separation
and/or component fracture.